Abstract

Sparse reconstructions based on minimizing l¹-norms have gained huge attention in signal and image processing, inverse problems, and compressed sensing recently. However, the overall sparsity enforced by minimal l¹-norm is not the only kind of prior information available in practice. Strong recent direction of research are related to unknowns being matrices, with prior information being e. g. low rank incorporated via nuclear norm minimization or block sparsity (or collaborative sparsity) incorporated by minimization of l^p,1-norms with p in (1,\infty).

In this talk we consider another type of sparsity-functionals, namely l^1,\infty-norms. Our motivation is a local sparsity that frequently appears in inversion with some spatial dimensions and at least one additional dimension such as time or spectral information in imaging.

First we will motivate the use of the l^1,\infty-norm as regularization functional for dictionary based reconstruction of matrix completion problems. Then we will reformulate the problem to make it easier accessible and analyze it with regard to exact recovery. In order to obtain computational results we will propose another reformulation of the problem. Finally some basic results will be presented using splitting techniques.